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研究生:郭雨甡
研究生(外文):Yu-shen Kuo
論文名稱:承受靜電力之微曲樑的吸附電壓解析解及其應用於反算薄膜之楊氏模數與應力梯度
論文名稱(外文):An Analytical Solution to the Pull-in Voltage of the Micro Curled Cantilever Beam subjected to Electrostatic Load and Its Application to Extract the Young’s Modulus and Stress Gradient of Thin Films
指導教授:黃世欽黃世欽引用關係
指導教授(外文):Shyh-Chin Huang
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:機械工程系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:104
中文關鍵詞:吸附電壓機械性質楊氏模數殘留應力
外文關鍵詞:residual stressYoung’s modulusmechanical propertypull-in voltage
相關次數:
  • 被引用被引用:1
  • 點閱點閱:615
  • 評分評分:
  • 下載下載:51
  • 收藏至我的研究室書目清單書目收藏:0
摘要
因微結構與靜電場之耦合(coupling)效應、靜電力的非線性、雜散電場(fringing field)效應、及應力梯度(stress gradient)所產生之預變形(pre-deformation)等,使得靜電式元件的分析相當複雜且不易求解。因此本研究目的在求解微曲樑結構承受靜電力作用下的吸附電壓(pull-in voltage);並由吸附電壓的解析解,建立一高精確度之演算法,可由量測微結構的吸附電壓,即可反算薄膜材料之楊氏模數與應力梯度。
首先以微結構在承受靜電力驅動時之彎曲應變能與雜散電場效應之電位能,推導出系統之總能量式,繼之以最小能量法搭配假設撓曲函數(assumed deflection shape function),以推導出微結構之吸附電壓的解析解。經與文獻及實驗結果比較,驗證解析解之誤差在1%以內,堪稱非常精確。本研究所推導出的吸附電壓解析解可應用於萃取薄膜材料之楊氏模數與應力梯度,只要量測出微結構的吸附電壓,即可採用該吸附電壓解析解反算出薄膜材料之楊氏模數與應力梯度。實驗驗證反算的楊氏模數與應力梯度之誤差小於2%,堪稱非常精確。本研究所建立的薄膜材料性質檢測方法完全採用電信號,即以電壓驅動微結構變形,而量測微結構之電容值,本法與IC檢測技術相容,適用於晶圓級檢測(wafer level testing)。
ABSTRACT
The analytical modeling of the electrostatic devices is quite complicated and difficult in virtue of such effects as the electric-mechanical coupling effect, the nonlinearity of the electrostatic force, the fringe field, and the pre-deformation of the micro-structure caused by the residual stress and stress gradient. This thesis aims at developing an analytical solution to the pull-in voltage of a micro curled cantilever beam subjected to electrostatic loads. High precision analytical solution to the pull-in voltage and its application to extract the young’s modulus and stress gradient of thin films is established in this thesis.
First of all, we use energy method to drive out the bending strain energy and fringing field effect electrical potential energy of the micro curled beam subjected to electrostatic loads. Continuously, the analytical solution to the pull-in voltage is derived based on the minimum energy method and assumed deflection shape function. Then one can use the aforesaid analytical solution of the pull-in voltage to extracted the Young’s modulus and stress gradient of the test structures. The accuracy and precision of the present method for extracting the Young’s modulus and residual stress is verified through comparing with the results conducted in the published works as well as the experiment conducted by the author. The error of the extracted Young’s modulus and stress gradient are below 2% compared to the experimentally measured data.
目錄
摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖表索引 VII
第一章 緒論 1
1.1 前言 1
1.2 研究動機 2
1.3 參考文獻 3
1.3.1 薄膜材料之楊氏模數的檢測技術 4
1.3.2 薄膜材料之殘留應力的檢測技術 10
1.4 研究目標 15
1.5 本文架構 16
第二章 承受靜電力之微曲樑的吸附電壓解析解 18
2.1 承受靜電力之微曲樑的能量式 18
2.2 吸附電壓 26
2.3 吸附電壓解析解之驗證 30
2.4 雜散電場效應之影響 36
第三章 承受靜電力之微曲樑的非線性靜電項降階函數式 41
3.1 降階模型 41
3.1.1 三階總能量式模型 (Third order model) 42
3.1.2 四階總能量式模型 (Fourth order model) 43
3.2 降階模型之吸附電壓 43
3.2.1 三階模型之吸附電壓 43
3.2.2 四階模型之吸附電壓 46
3.3 數值分析與討論 50
第四章 以微測試結構之吸附電壓反算薄膜材料之楊氏模數與應力梯 55
4.1 以微測試結構之吸附電壓反算薄膜之楊氏模數 56
4.2 以微測試結構之吸附電壓反算薄膜之應力梯度 56
4.3 薄膜材料之楊氏模數與應力梯度演算法的驗證 60
第五章 實驗方法 66
5.1 微懸臂樑之製程 66
5.2 吸附電壓量測方法 75
5.2.1 電容-電壓量測原理 75
5.2.2 實驗量測儀器之參數設定 75
5.2.3 量測儀器之校正 78
第六章 實驗結果與討論 79
6.1 鋁懸臂樑之吸附電壓量測 79
6.2 濺鍍鋁薄膜之楊氏模數與應力梯度的萃取 82
6.3 厚度誤差的影響 85
第七章 結論與未來展望 94
7.1 結論 95
7.2 未來展望 96
參考文獻 97
符號說明 102
作者簡介 104
參考文獻
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